Q. 68 - Intermediate Algebra

Question

In the following exercises, simplify using absolute value signs as needed.$\sqrt{m^{13}},\sqrt[5]{u^7},\sqrt[6]{v^{11}}$

Step-by-Step Solution

Answer

The expression in simplified form is $m\sqrt[6]{m},u\sqrt[5]{u^2},v\sqrt[6]{v^5}$

Step 1: Given information

Given the expression $\sqrt{m^{13}},\sqrt[5]{u^7},\sqrt[6]{v^{11}}$

Step 2: Using the product property

Using the product property, we get

$$\begin{gathered} \sqrt{m^{13}}=\sqrt{m^{12}m} \\ \sqrt{m^{13}}=\sqrt{m^{12}}\sqrt{m} \\ \sqrt{m^{13}}=m^6\sqrt{m} \end{gathered}$$m

Step 3: Using the product property

Using the property, we get

$$\begin{gathered} \sqrt[5]{u^7}==\sqrt[5]{u^5{u}^2} \\ \sqrt[5]{u^7}=\sqrt[5]{u^5}\sqrt[5]{u^2} \\ \sqrt[5]{u^7}=u\sqrt[5]{u^2} \end{gathered}$$

Step 4: Using the property

Using the property, we have

$$\begin{gathered} \sqrt[6]{v^{11}}=\sqrt[6]{v^6{v}^5} \\ \sqrt[6]{v^{11}}=\sqrt[6]{v^6}\sqrt[6]{v^5} \\ \sqrt[6]{v^{11}}=v\sqrt[6]{v^5} \end{gathered}$$